Expected Value

Expected value is the probability-weighted average of outcomes when the expectation exists. It summarizes a distribution but need not be a possible or likely individual result.

Expected value is a probability-weighted average, defined by summing or integrating outcomes when the expectation exists. It need not equal any possible single outcome, and it does not describe the spread or the worst case. Linearity makes expectations useful for totals even when the components are dependent, provided the relevant expectations are defined.

Whether to maximize expected money, expected utility, or another objective is a separate decision-model choice. Repeated opportunities can help explain averages under suitable conditions but are not required for expectation to be meaningful. A one-time decision still has an expectation, while loss limits, nonlinear preferences, and survival constraints can make expected money alone inadequate.

When to use it

When analyzing data; when building predictive models; when evaluating statistical claims; when quantifying uncertainty.

How it can help

Calculate the weighted average, then examine variability, constraints, and adverse outcomes. Decide whether expected money, utility, or another criterion fits the decision.